I agree with Keef

The Stones are in town(LA) for 2 nights.

With so many things now being now deemed "inappropriate" these days, I suppose this isn't a surprise?

Brown Sugar is part of the Stones "permanent set list".  
This cancel culture does raise some tricky issues all by itself; its mere existence is disconcerting for some on a number of levels.

But self-censorship?  The Stones?  Huh?  Where will it stop?

I wonder about the reception some of their other songs receive, like "It Must be Hell"?  That is much more subversive.  Many others.
Censorship of the arts within the private (as opposed to governmental/government funded public) realm is just bad news 99% of the time, IMO.  If the ‘Stones want to self-censor on this, I suppose it’s their right and it’d be a whole other animal indeed if this were a case of the song being performed on any part of any taxpayer’s tax-dime (????).  Same issues dealt with in recent years in the visual arts (Eric Fischl, Andres Serrano, et al…).
A rock band dropping one of its many hits from its live set list is hardly an example of "cancel culture."

The Stones are part of the generation which represents "doing their own thing"  

I think it's more of a PR thing to align more with $ponsor$, who hold the bag. They can't to upset the new rule.